Ian Agol, Nathan M. Dunfield, Peter A. Storm, William P. Thurston
Published 2005-06-17Version 2
We prove a volume inequality for 3-manifolds having C^0 metrics "bent" along a hypersurface, and satisfying certain curvature pinching conditions. The result makes use of Perelman's work on Ricci flow and geometrization of closed 3-manifolds. Corollaries include a new proof of a conjecture of Bonahon about volumes of convex cores of Kleinian groups, improved volume estimates for certain Haken hyperbolic 3-manifolds, and a lower bound on the minimal volume orientable hyperbolic 3-manifold. An appendix by Dunfield compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.
Comments: 25 pages, 9 figures; main text by Agol, Storm, Thurston, with an appendix by Dunfield
Journal: J. Amer. Math. Soc. 20 (2007), no. 4, 1053-1077
Estimates on the Lower Bound of the First Gap
Lower Bound for the Simplicial Volume of Closed Manifolds Covered by $\mathbb{H}^{2}\times\mathbb{H}^{2}\times\mathbb{H}^{2}$
Diameters of 3-Sphere Quotients
![QR code for arXiv:math/0506338 [math.DG]](http://oss.arxitics.com/images/favicon.svg)